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arXiv:2601.22401cs.AI

Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems

Tony Feng, Trieu Trinh, Garrett Bingham, Jiwon Kang, Shengtong Zhang, Sang-hyun Kim, Kevin Barreto, Carl Schildkraut, Junehyuk Jung, Jaehyeon Seo, Carlo Pagano, Yuri Chervonyi, Dawsen Hwang, Kaiying Hou, Sergei Gukov, Cheng-Chiang Tsai, Hyunwoo Choi, Youngbeom Jin, Wei-Yuan Li, Hao-An Wu, Ruey-An Shiu, Yu-Sheng Shih, Quoc V. Le, Thang Luong

Abstract

We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's Erdős Problems database. We employ a hybrid methodology: AI-driven natural language verification to narrow the search space, followed by human expert evaluation to gauge correctness and novelty. We address 13 problems that were marked 'Open' in the database: 5 through seemingly novel autonomous solutions, and 8 through identification of previous solutions in the existing literature. Our findings suggest that the 'Open' status of the problems was through obscurity rather than difficulty. We also identify and discuss issues arising in applying AI to math conjectures at scale, highlighting the difficulty of literature identification and the risk of ''subconscious plagiarism'' by AI. We reflect on the takeaways from AI-assisted efforts on the Erdős Problems.

arXiv comments
Reclassify Erdos-935 as Independent Rediscovery, bringing the number of autonomous solutions down to 5. (Explanation in Addendum 4.1) Elaborate on Footnote 3. Slightly reword various phrases in the Introduction in response to feedback
Journal reference
DOI
Subjects
cs.AIArtificial Intelligence math.COCombinatorics math.NTNumber Theory

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Linked by 2 identifiable commenters in 2 comments across 2 threads, from Feb 2026 to Mar 2026. Found in 1 HN submission from Feb 2026 to Feb 2026. Open submission discussions.

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Discussed in comments2 threads

  1. Claude's Cycles [pdf] 1 comment

    • Hold your horses, that’s a long way off. The best math AI tool we currently have, Aletheia, was only able to solve 13 out of 700 attempted open Erdos problems, only 4 of which were solved autonomously: https://arxiv.org/html/2601.22401v3 Clearly, these models still struggle with…

      emp17344View on HNParent context

  2. GPT-5.2 derives a new result in theoretical physics 1 comment

    • The erdosproblems website shows 851 was proved in 1934. https://www.erdosproblems.com/851 I guess 1051 qualifies - from the paper: "Semi-autonomous mathematical discovery with gemini" https://arxiv.org/pdf/2601.22401 "We tentatively believe Aletheia’s solution to Erdős-1051…

      carefree-bobView on HNParent context

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